Presumably, ln⁵(<em>x</em>) is the same as (ln(<em>x</em>))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(<em>x</em>)))))).
Then substituting <em>u</em> = ln(<em>x</em>) and d<em>u</em> = d<em>x</em>/<em>x</em> gives
![\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cfrac%7B%5Cmathrm%20dx%7D%7Bx%5Cln%5E5%28x%29%7D%20%3D%20%5Cint%5Cfrac%7B%5Cmathrm%20du%7D%7Bu%5E5%7D%20%3D%20-%5Cfrac1%7B4u%5E4%7D%2BC%20%3D%20%5Cboxed%7B-%5Cfrac1%7B4%5Cln%5E4%28x%29%7D%2BC%7D)
![\dfrac{1}{6} \text{ of } 5](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%7D%7B6%7D%20%5Ctext%7B%20of%20%7D%205%20)
"of" is written as "x" in number statement:
![= \dfrac{1}{6} \times 5](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B1%7D%7B6%7D%20%5Ctimes%205)
Write 5 as fraction:
![= \dfrac{1}{6} \times \dfrac{5}{1}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B1%7D%7B6%7D%20%5Ctimes%20%20%5Cdfrac%7B5%7D%7B1%7D%20)
Multiply:
Answer:
The value of the variable=13 meters
Step-by-step explanation:
Step 1
Express the dimensions of the pool
Length=7+x
width=6
Step 2
Express the area of a rectangle as shown;
A=L×W
where;
A=area of a rectangle
L=length of the rectangle
W=width of the rectangle
In our case;
A=120 m²
L=x+7
W=6
replacing in the equation;
120 m²=(x+7)×6
120=6 x+42
6 x+42=120
6 x=120-42
6 x=78
x=78/6
x=13
The value of the variable=x=13 meters
The theoretical probability is the probability you'd expect before performing the experiment. So, assuming the die is fair, every outcome has the same probability. Since there are 6 numbers on the die, every number appears, theoretically, with probability 1/6.
The experimental probability is the probability you estimate after performing the experiment. You divide the number of cases a certain outcome happened, and divide by the total number of trials.
In this case, you performed 50 rolls, and the die landed on six 12 times. This means that the experimental probability is 12/50, or 6/25.
Answer:
140.571
7 | 984.000
98
__
00 40
35
__
050
49
___
010
7
__
1
Step-by-step explanation:
The numbers listed below 984 is the product of 7 and the number above it.
I hope this helps! :)